Numbering Systems & Place Values

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Place Value Chart (from Trillions down to Quintillionths)
American Numbering System
Googol and Googolplex
British Numbering System
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Copyright Information

Place Values from Trillions down to Quintillionths

If you study this pattern, and the list of larger number names further down, you should be able to create your own chart going as high, and as small, as you'd like to go.

Write your whole number (or the whole number part of your number) into the boxes above so that the last digit of your number goes just before the decimal point. Then read each group of three digits as a regular three-digit number, followed by the number word for the group, if any. For example, the number 123,456,789 would be read as "one hundred twenty three million, four hundred fifty-six thousand, seven hundred eighty nine."

If there is a both a whole number and a decimal part of the number, we read the decimal point as the word "and".

To read the value of the decimal part of the number, we read the entire number after the decimal point, as if the values weren't there, but as if it were a whole number, then we read the place value for the last digit that we have in our number. I would read the number 12.34567 as "twelve AND thirty-four thousand five hundred sixty-seven hundred-thousandths." (Return to top)

American Numbering System

Here is the entire chart of all the number names (I know of) in the American Numbering System. Note that the British Numbering System does not match the American system after the millions. Thousands and Millions match, but then the British system has milliards, billions, billiards, trillions, trilliards, etc.

Our numbering system is based on LATIN. The latin words for the various numbers give us the prefixes bi-, tri-, quad-, quint-, sex-, sept-, oct-, non-, dec-, which tells us the number of sets of zeroes after 1,000 in billion (2), trillion (3), quadrillion (4), quintillion (5), sextillion (6), septillion (7), octillion (8), nonillion (9), and decillion (10). Similar Latin words give us the rest of our numbering system. Prefixes un-, duo-, tre-, quattuor, quin-, sex-, sept-, octo, and novem-, appear to modify decillion to give us the numbers undecillion up to novemdecillion. I followed the same pattern to create the words unvigintillion up to novemvigintillion. I referred to Latin sources to create the number words trigintillion,

I have listed this chart by the number of sets of ",000" after one thousand. Learn this pattern for "bi-tri-quad-quint" and you'll have your first set of big numbers memorized:

number
of
000's
after
thou-
sand    Name     sample of number (or how to write "one" of it)
====--=========--==================================================
    thousand     1,000
 1  million      1,000,000
 2  billion      1,000,000,000
 3  trillion     1,000,000,000,000
 4  quadrillion  1,000,000,000,000,000
 5  quintillion  1,000,000,000,000,000,000
 6  sextillion   1,000,000,000,000,000,000,000
 7  septillion   1,000,000,000,000,000,000,000,000
 8  octillion    1,000,000,000,000,000,000,000,000,000
 9  nonillion    1,000,000,000,000,000,000,000,000,000,000
10  decillion    1,000,000,000,000,000,000,000,000,000,000,000
11  undecillion  1,000,000,000,000,000,000,000,000,000,000,000,000
12  duodecillion 1,000,000,000,000,000,000,000,000,000,000,000,000,000
13  tredecillion        write 1,000 followed by 13 groups of three zeros
14  quattuordecillion         1,000 followed by 14 groups of three zeros
15  quindecillion             1,000 followed by 15 groups of three zeros
16  sexdecillion              1,000 followed by 16 groups of three zeros
17  septendecillion           1,000 followed by 17 groups of three zeros
18  octodecillion             1,000 followed by 18 groups of three zeros
19  novemdecillion            1,000 followed by 19 groups of three zeros
20  vigintillion              1,000 followed by 20 groups of three zeros
21  unvigintillion            1,000 followed by 21 groups of three zeros
22  duovigintillion           1,000 followed by 22 groups of three zeros
23  trevigintillion           1,000 followed by 23 groups of three zeros
24  quattuorvigintillion      1,000 followed by 24 groups of three zeros
25  quinvigintillion          1,000 followed by 25 groups of three zeros
26  sexvigintillion           1,000 followed by 26 groups of three zeros
27  septenvigintillion        1,000 followed by 27 groups of three zeros
28  octovigintillion          1,000 followed by 28 groups of three zeros
29  novemvigintillion         1,000 followed by 29 groups of three zeros
30  trigintillion             1,000 followed by 30 groups of three zeros
31  untrigintillion           1,000 followed by 31 groups of three zeros
32  duotrigintillion          1,000 followed by 32 groups of three zeros
33  tretrigintillion          1,000 followed by 33 groups of three zeros
34  quattuortrigintillion     1,000 followed by 34 groups of three zeros
35  quintrigintillion         1,000 followed by 35 groups of three zeros
36  sextrigintillion          1,000 followed by 36 groups of three zeros
37  septentrigintillion       1,000 followed by 37 groups of three zeros
38  octotrigintillion         1,000 followed by 38 groups of three zeros
39  novemtrigintillion        1,000 followed by 39 groups of three zeros
40  quadragintillion          1,000 followed by 40 groups of three zeros (quardragintillion?)
41  unquadragintillion        1,000 followed by 41 groups of three zeros
42  duoquadragintillion       1,000 followed by 42 groups of three zeros
43  trequadragintillion       1,000 followed by 43 groups of three zeros
44  quattuorquadragintillion  1,000 followed by 44 groups of three zeros
45  quinquadragintillion      1,000 followed by 45 groups of three zeros
46  sexquadragintillion       1,000 followed by 46 groups of three zeros
47  septenquadragintillion    1,000 followed by 47 groups of three zeros
48  octoquadragintillion      1,000 followed by 48 groups of three zeros
49  novemquadragintillion     1,000 followed by 49 groups of three zeros
50  quinquagintillion         1,000 followed by 50 groups of three zeros
51  unquinquagintillion       1,000 followed by 51 groups of three zeros
52  duoquinquagintillion      1,000 followed by 52 groups of three zeros
53  trequinquagintillion      1,000 followed by 53 groups of three zeros
54  quattuorquinquagintillion 1,000 followed by 54 groups of three zeros
55  quinquinquagintillion     1,000 followed by 55 groups of three zeros
56  sexquinquagintillion      1,000 followed by 56 groups of three zeros
57  septenquinquagintillion   1,000 followed by 57 groups of three zeros
58  octoquinquagintillion     1,000 followed by 58 groups of three zeros
59  novemquinquagintillion    1,000 followed by 59 groups of three zeros
60  sexagintillion            1,000 followed by 60 groups of three zeros
61  unsexagintillion          1,000 followed by 61 groups of three zeros
62  duosexagintillion         1,000 followed by 62 groups of three zeros
63  tresexagintillion         1,000 followed by 63 groups of three zeros
64  quattuorsexagintillion    1,000 followed by 64 groups of three zeros
65  quinsexagintillion        1,000 followed by 65 groups of three zeros
66  sexsexagintillion         1,000 followed by 66 groups of three zeros
67  septensexagintillion      1,000 followed by 67 groups of three zeros
68  octosexagintillion        1,000 followed by 68 groups of three zeros
69  novemsexagintillion       1,000 followed by 69 groups of three zeros
70  septuagintillion          1,000 followed by 70 groups of three zeros
71  unseptuagintillion        1,000 followed by 71 groups of three zeros
72  duoseptuagintillion       1,000 followed by 72 groups of three zeros
73  treseptuagintillion       1,000 followed by 73 groups of three zeros
74  quattuorseptuagintillion  1,000 followed by 74 groups of three zeros
75  quinseptuagintillion      1,000 followed by 75 groups of three zeros
76  sexseptuagintillion       1,000 followed by 76 groups of three zeros
77  septenseptuagintillion    1,000 followed by 77 groups of three zeros
78  octoseptuagintillion      1,000 followed by 78 groups of three zeros
79  novemseptuagintillion     1,000 followed by 79 groups of three zeros
80  octogintillion            1,000 followed by 80 groups of three zeros
81  unoctogintillion          1,000 followed by 81 groups of three zeros
82  duooctogintillion         1,000 followed by 82 groups of three zeros
83  treoctogintillion         1,000 followed by 83 groups of three zeros
84  quattuoroctogintillion    1,000 followed by 84 groups of three zeros
85  quinoctogintillion        1,000 followed by 85 groups of three zeros
86  sexoctogintillion         1,000 followed by 86 groups of three zeros
87  septoctogintillion        1,000 followed by 87 groups of three zeros
88  octooctogintillion        1,000 followed by 88 groups of three zeros
89  novemoctogintillion       1,000 followed by 89 groups of three zeros
90  nonagintillion            1,000 followed by 90 groups of three zeros
91  unnonagintillion          1,000 followed by 91 groups of three zeros
92  duononagintillion         1,000 followed by 92 groups of three zeros
93  trenonagintillion         1,000 followed by 93 groups of three zeros
94  quattuornonagintillion    1,000 followed by 94 groups of three zeros
95  quinnonagintillion        1,000 followed by 95 groups of three zeros
96  sexnonagintillion         1,000 followed by 96 groups of three zeros
97  septennonagintillion      1,000 followed by 97 groups of three zeros
98  octononagintillion        1,000 followed by 98 groups of three zeros
99  novemnonagintillion       1,000 followed by 99 groups of three zeros
100 centillion                1,000 followed by 100 groups of three zeros
One GOOGOL is a ONE followed by 100 zeroes.
One GOOGOLPLEX is a ONE followed by one googol zeroes.
        (you can't write a googolplex, even in a million years)

All of the large number names up to vigintillion, and the names centillion, googol, and googolplex, come from numerous encyclopedias and dictionaries.

All of the large number names from unvigintillion up to novemnonagintillion were coined (created) by John Knoderer (webmaster (at) mazes.com).

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Googols and Googolplexes

What is a googol?

one googol is equal to ten, raised to the one hundredth power. It is written as a one followed by one hundred zeroes. This is a googol:

10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

What is a googolplex?

one "googolplex" is equal to ten raised to the googol power. If it were to be written out, it would be a one followed by one googol zeroes.

One googolplex equals 10 raised to the 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 power.

One googolplex is written as a one followed by 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 zeroes.

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British Numbering System

There is a fascinating article in Compton's Living Encyclopedia (AOL keyword: ENCYCLOPEDIA) that compares the American Numbering System with the British Numbering System. Once you get past eight zeroes, the names do not match. For example, a number followed by 9 zeroes is in the British "milliards" but the American "trillions".

In other words, the British Numbering System is completely different from the American Numbering System after the thousands and millions. Thousand and Million are the same, but then you see Milliard, Billion, Billiard, Trillion, Trilliard, etc.

However, we do have to give the British Credit. They are using the ORIGINAL numbering system, based on powers of a million. Over 200 years ago, the French corrupted the system, changing it to powers of a thousand. Personally, I like the corrupted version better.

TRIVIA QUESTION: If a "Billiard" is a one followed by 15 zeroes in the British System, then does this mean that is where we got the name of the game BILLIARDS, which is played with a cue ball and 15 numbered balls? If someone knows, please let me know.

#   *Power*
of   of  a
0s  Million  Name       samples of some of them
==--=======--==================
3            thousand     1,000
6      1     million      1,000,000
9            milliard     1,000,000,000
12     2     billion      1,000,000,000,000
15           billiard     1,000,000,000,000,000
18     3     trillion     1,000,000,000,000,000,000   
21           trilliard    1,000,000,000,000,000,000,000
24     4     quadrillion  1,000,000,000,000,000,000,000,000
27           quadrilliard 1,000,000,000,000,000,000,000,000,000
30     5     quintillion  1,000,000,000,000,000,000,000,000,000,000
33           quintilliard 1,000,000,000,000,000,000,000,000,000,000,000
36     6     sextillion   1,000,000,000,000,000,000,000,000,000,000,000,000
39           sextilliard
42     7     septillion    NOTE that if you divide the # of zeroes by six,
45           septilliard   you have the number that relates to the word of
48     8     octillion     the group.  2=bi, 3=tri, 4=quad, 5=quin, 6=sex,
51           octilliard    7=sept, 8=oct, 9=non, 10=decem, 20=viginti.
54     9     nonillion
57           nonilliard              the names for number groups
60    10     decillion               3, 6, 9, 12, and every multiple
63           decilliard              of 6 up to 120 came from
66    11     undecillion             several sources, both dictionary
69           undecilliard            and encyclopedic.
72    12     duodecillion
75           duodecilliard           I followed the pattern of
78    13     tredecillion            "million" to "milliard" to list
81           tredecilliard           all other groups up to 123.
84    14     quattuordecillion
87           quattuordecilliard    The prefixes un-, duo-, tre-, quattuor-,
90    15     quindecillion         quin-, sex-, septen, octo-, and novem-
93           quindecilliard        appear to modify the latin TEN (decem),
96    16     sexdecillion          to make 11, 12, up to 19.
99           sexdecilliard
135   17     septendecillion
105          septendecilliard
108   18     octodecillion
111          octodecilliard
114   19     novemdecillion
117          novemdecilliard
120   20     vigintillion
123          vigintilliard
126   21     unvigintillion           I followed the prefix-pattern
129          unvigintilliard          used before -decillion and
132   22     duovigintillion          -decilliard to create the names
135          duovigintilliard         for 126 to 177, 21 through 29
138   23     trevigintillion          groups of six.
141          trevigintilliard
144   24     quattuorvigintillion
147          quattuorvigintilliard
150   25     quinvigintillion
153          quinvigintilliard
156   26     sexvigintillion
159          sexvigintilliard
162   27     septenvigintillion
165          septenvigintilliard
168   28     octovigintillion
171          octovigintilliard
174   29     novemvigintillion
177          novemvigintilliard
180   30     trigintillion
183          trigintilliard
186   31     untrigintillion
189          untrigintilliard
192   32     duotrigintillion
195          duotrigintilliard
198   33     tretrigintillion
201          tretrigintilliard
204   34     quattuortrigintillion
207          quattuortrigintilliard
210   35     quintrigintillion
213          quintrigintilliard
216   36     sextrigintillion
219          sextrigintilliard
222   37     septentrigintillion
225          septentrigintilliard
228   38     octotrigintillion
231          octotrigintilliard
234   39     novemtrigintillion
237          novemtrigintilliard
240   40     quadragintillion
243          quadragintilliard
246   41     unquadragintillion
249          unquadragintilliard
252   42     duoquadragintillion
255          duoquadragintilliard
258   43     trequadragintillion
261          trequadragintilliard
264   44     quattuorquadragintillion
267          quattuorquadragintilliard
270   45     quinquadragintillion
273          quinquadragintilliard
276   46     sexquadragintillion
279          sexquadragintilliard
282   47     septenquadragintillion
285          septenquadragintilliard
288   48     octoquadragintillion
291          octoquadragintilliard
294   49     novemquadragintillion
297          novemquadragintilliard
300   50     quinquagintillion
303          quinquagintilliard
306   51     unquinquagintillion
309          unquinquagintilliard
312   52     duoquinquagintillion
315          duoquinquagintilliard
318   53     trequinquagintillion
321          trequinquagintilliard
324   54     quattuorquinquagintillion
327          quattuorquinquagintilliard
330   55     quinquinquagintillion
333          quinquinquagintilliard
336   56     sexquinquagintillion
339          sexquinquagintilliard
342   57     septenquinquagintillion
345          septenquinquagintilliard
348   58     octoquinquagintillion
351          octoquinquagintilliard
354   59     novemquinquagintillion
357          novemquinquagintilliard
360   60     sexagintillion
363          sexagintilliard
366   61     unsexagintillion
369          unsexagintilliard
372   62     duosexagintillion
375          duosexagintilliard
378   63     tresexagintillion
381          tresexagintilliard
384   64     quattuorsexagintillion
387          quattuorsexagintilliard
390   65     quinsexagintillion
393          quinsexagintilliard
396   66     sexsexagintillion
399          sexsexagintilliard
435   67     septensexagintillion
405          septensexagintilliard
408   68     octosexagintillion
411          octosexagintilliard
414   69     novemsexagintillion
417          novemsexagintilliard
420   70     septuagintillion
423          septuagintilliard
426   71     unseptuagintillion
429          unseptuagintilliard
432   72     duoseptuagintillion
435          duoseptuagintilliard
438   73     treseptuagintillion
441          treseptuagintilliard
444   74     quattuorseptuagintillion
447          quattuorseptuagintilliard
450   75     quinseptuagintillion
453          quinseptuagintilliard
456   76     sexseptuagintillion
459          sexseptuagintilliard
462   77     septenseptuagintillion
465          septenseptuagintilliard
468   78     octoseptuagintillion
471          octoseptuagintilliard
474   79     novemseptuagintillion
477          novemseptuagintilliard
480   80     octogintillion
483          octogintilliard
486   81     unoctogintillion
489          unoctogintilliard
492   82     duooctogintillion
495          duooctogintilliard
498   83     treoctogintillion
501          treoctogintilliard
504   84     quattuoroctogintillion
507          quattuoroctogintilliard
510   85     quinoctogintillion
513          quinoctogintilliard
516   86     sexoctogintillion
519          sexoctogintilliard
522   87     septoctogintillion
525          septoctogintilliard
528   88     octooctogintillion
531          octooctogintilliard
534   89     novemoctogintillion
537          novemoctogintilliard
540   90     nonagintillion
543          nonagintilliard
546   91     unnonagintillion
549          unnonagintilliard
552   92     duononagintillion
555          duononagintilliard
558   93     trenonagintillion
561          trenonagintilliard
564   94     quattuornonagintillion
567          quattuornonagintilliard
570   95     quinnonagintillion
573          quinnonagintilliard
576   96     sexnonagintillion
579          sexnonagintilliard
582   97     septennonagintillion
585          septennonagintilliard
588   98     octononagintillion
591          octononagintilliard
594   99     novemnonagintillion
597          novemnonagintilliard
600  100     centillion
603          centilliard

I don't know if the terms Googol and Googolplex are used in the British Numbering System. Since there were coined by American Mathematicians in 1929 and 1935, it is likely that they are not officially used in the U.K., but unofficially, I'm sure that some of them use it for fun.

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About the Author

You can find some of his puzzles on his web page at www.MAZES.com. John has written materials that can help people get ready for the Driver's License exam. You can find these materials at www.DriverExam.org.

John is a computer programmer, consultant, web page designer, teacher, tutor and puzzle creator. John telecommutes throughout the world and is available to work for you. Please e-mail (webmaster (at) mazes.com).

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Copyright Information

If you use information from a source like this in a report, you should give proper credit, citing the author as a source. In other words, you must acknowledge where you found the information and who supplied it. This is a matter of professional courtesy. Here is an example of a footnote:

Footnote Example:
* John Knoderer, [webmaster (at) mazes.com], "American Numbering System and Place Values,"http:// www.mazes.com/AmericanNumberingSystem.html, September 10, 1997; revised May 21, 1999.

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